Question

in a cylindrical vessel of radius 10cm, containing some water,9000small sperical balls are dropped which are completely immersed in water which raises water level .if each sperical ball is of radius 0.5cm, then find the raise in the level of water in vessel.​

Answer 1

Answer:

volume of balls=9000*4/3*π(0.5)^3

let height risen be h

volume risen = volume of balls

π*(10)^2 *h= 9000*4/3π *(0.5)^3

h=15cm

Answer 2

The height of the cylindrical vessel is 15 cm .

Step-by-step explanation:

Given as :

The radius of cylinder vessel = r = 10 cm

The height of the cylinder vessel = h cm

9000 small spherical balls are dropped which are completely immersed in water which raises water level

The radius of sphere balls = R = 0.5 cm

The number of balls = N = 9000

Let The raise in water level in cylinder =  height of the cylinder vessel = h cm

Let The volume of spherical balls = V cubic cm

Let The volume of cylinder vessel = v cubic cm

According to question

∵ Volume of spherical balls =  $\dfrac{4}{3}$ × π × radius³

Or,  V =  $\dfrac{4}{3}$ × π × R³

Or,  V =  $\dfrac{4}{3}$ × 3.14 × (0.5 cm)³

Or,  V =  $\dfrac{4}{3}$ × 3.14 × 0.125 cm³

∴  Volume = V = 0.5233    cm³

Again

∵   Volume of cylindrical vessel =  π × radius² × height

Or,  v = π × r² × h

Or,  v = 3.14 × (10 cm)² × h

∴     v = 3.14 × 100 cm² × h

i.e   volume = v = 314 h   cm²

Again

Number of balls dropped inside vessel = $\dfrac{volume of vessel}{volume of ball}$

Or,   N = $\dfrac{v}{V}$

Or, 9000 = $\dfrac{314h}{0.5233}$

Or, 314 ×  h = 9000 × 0.5233

Or,  314 ×  h = 4709.7

∴               h = $\dfrac{4709.7}{314}$

i.e             h = 14.99 ≈  15 cm

So, The height of the cylindrical vessel = h = 15 cm

Hence, The height of the cylindrical vessel is 15 cm . Answer